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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numeric_odeint.odeint_in_detail.using_boost__range"></a><a class="link" href="using_boost__range.html" title="Using boost::range">Using
      boost::range</a>
</h3></div></div></div>
<p>
        Most steppers in odeint also accept the state give as a range. A range is
        sequence of values modeled by a range concept. See <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>
        for an overview over existing concepts and examples of ranges. This means
        that the <code class="computeroutput"><span class="identifier">state_type</span></code> of the
        stepper need not necessarily be used to call the <code class="computeroutput"><span class="identifier">do_step</span></code>
        method.
      </p>
<p>
        One use-case for <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>
        in odeint has been shown in <a class="link" href="../tutorial/chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">Chaotic
        System</a> where the state consists of two parts: one for the original
        system and one for the perturbations. The ranges are used to initialize (solve)
        only the system part where the perturbation part is not touched, that is
        a range consisting only of the system part is used. After that the complete
        state including the perturbations is solved.
      </p>
<p>
        Another use case is a system consisting of coupled units where you want to
        initialize each unit separately with the ODE of the uncoupled unit. An example
        is a chain of coupled van-der-Pol-oscillators which are initialized uniformly
        from the uncoupled van-der-Pol-oscillator. Then you can use <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>
        to solve only one individual oscillator in the chain.
      </p>
<p>
        In short, you can <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>
        to use one state within two system functions which expect states with different
        sizes.
      </p>
<p>
        An example was given in the <a class="link" href="../tutorial/chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">Chaotic
        System</a> tutorial. Using Boost.Range usually means that your system
        function needs to adapt to the iterators of Boost.Range. That is, your function
        is called with a range and you need to get the iterators from that range.
        This can easily be done. You have to implement your system as a class or
        a struct and you have to templatize the <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>. Then you can use the <code class="computeroutput"><span class="identifier">range_iterator</span></code>-meta
        function and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span></code> and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">end</span></code> to
        obtain the iterators of your range:
      </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">class</span> <span class="identifier">sys</span>
<span class="special">{</span>
    <span class="keyword">template</span><span class="special">&lt;</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Deriv</span> <span class="special">&gt;</span>
    <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&amp;</span><span class="identifier">x_</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">&amp;</span><span class="identifier">dxdt_</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span>
    <span class="special">{</span>
         <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special">&lt;</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">x_</span> <span class="special">);</span>
         <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special">&lt;</span> <span class="identifier">Deriv</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">dxdt</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">dxdt_</span> <span class="special">);</span>

         <span class="comment">// fill dxdt</span>
    <span class="special">}</span>
<span class="special">};</span>
</pre>
<p>
      </p>
<p>
        If your range is a random access-range you can also apply the bracket operator
        to the iterator to access the elements in the range:
</p>
<pre class="programlisting"><span class="keyword">class</span> <span class="identifier">sys</span>
<span class="special">{</span>
    <span class="keyword">template</span><span class="special">&lt;</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Deriv</span> <span class="special">&gt;</span>
    <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&amp;</span><span class="identifier">x_</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">&amp;</span><span class="identifier">dxdt_</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span>
    <span class="special">{</span>
         <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special">&lt;</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">x_</span> <span class="special">);</span>
         <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special">&lt;</span> <span class="identifier">Deriv</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">dxdt</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">dxdt_</span> <span class="special">);</span>

         <span class="identifier">dxdt</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">f1</span><span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">);</span>
         <span class="identifier">dxdt</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">f2</span><span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">);</span>
    <span class="special">}</span>
<span class="special">};</span>
</pre>
<p>
      </p>
<p>
        The following two tables show which steppers and which algebras are compatible
        with <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>.
      </p>
<div class="table">
<a name="boost_numeric_odeint.odeint_in_detail.using_boost__range.steppers_supporting_boost_range"></a><p class="title"><b>Table 1.9. Steppers supporting Boost.Range</b></p>
<div class="table-contents"><table class="table" summary="Steppers supporting Boost.Range">
<colgroup><col></colgroup>
<thead><tr><th>
                <p>
                  Stepper
                </p>
              </th></tr></thead>
<tbody>
<tr><td>
                <p>
                  adams_bashforth_moulton
                </p>
              </td></tr>
<tr><td>
                <p>
                  bulirsch_stoer_dense_out
                </p>
              </td></tr>
<tr><td>
                <p>
                  bulirsch_stoer
                </p>
              </td></tr>
<tr><td>
                <p>
                  controlled_runge_kutta
                </p>
              </td></tr>
<tr><td>
                <p>
                  dense_output_runge_kutta
                </p>
              </td></tr>
<tr><td>
                <p>
                  euler
                </p>
              </td></tr>
<tr><td>
                <p>
                  explicit_error_generic_rk
                </p>
              </td></tr>
<tr><td>
                <p>
                  explicit_generic_rk
                </p>
              </td></tr>
<tr><td>
                <p>
                  rosenbrock4_controller
                </p>
              </td></tr>
<tr><td>
                <p>
                  rosenbrock4_dense_output
                </p>
              </td></tr>
<tr><td>
                <p>
                  rosenbrock4
                </p>
              </td></tr>
<tr><td>
                <p>
                  runge_kutta4_classic
                </p>
              </td></tr>
<tr><td>
                <p>
                  runge_kutta4
                </p>
              </td></tr>
<tr><td>
                <p>
                  runge_kutta_cash_karp54_classic
                </p>
              </td></tr>
<tr><td>
                <p>
                  runge_kutta_cash_karp54
                </p>
              </td></tr>
<tr><td>
                <p>
                  runge_kutta_dopri5
                </p>
              </td></tr>
<tr><td>
                <p>
                  runge_kutta_fehlberg78
                </p>
              </td></tr>
<tr><td>
                <p>
                  symplectic_euler
                </p>
              </td></tr>
<tr><td>
                <p>
                  symplectic_rkn_sb3a_mclachlan
                </p>
              </td></tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_numeric_odeint.odeint_in_detail.using_boost__range.algebras_supporting_boost_range"></a><p class="title"><b>Table 1.10. Algebras supporting Boost.Range</b></p>
<div class="table-contents"><table class="table" summary="Algebras supporting Boost.Range">
<colgroup><col></colgroup>
<thead><tr><th>
                <p>
                  algebra
                </p>
              </th></tr></thead>
<tbody>
<tr><td>
                <p>
                  range_algebra
                </p>
              </td></tr>
<tr><td>
                <p>
                  thrust_algebra
                </p>
              </td></tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
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